what is the implied domain and range arccos(2cosec(x)-3)

[M-D]

hi,

what would be the implied domain and range of arccos(2cosec(x)-3)?

i got dom=[pi/3,5pi/6] and ran=[0,pi] is it correct?

thanks

[leflyi]

arcos has domain of [-1,1] and range [0, pi]


hmm

the implied domain of Cos whilst is [-1,1], and range [0, pi] in order for it to become inverse....

So...
arcos(2cos(x)-3)

would have the domain [-1,1] as there is no horizontal translation or dialation of y
and have the range [-3, 2pi-3]

however,

I could be completely wrong..

So feel free to correct me..

[M-D]

sorry i made a mistake in the question. the question actually is arccos(2cosec(x)-3).

i'll correct it in my initial post

[Lasercookie]

So for arccos(x)


For arccos(2cosec(x)-3):






cosec(x) is equal to 1 when where n is an integer.
When cosec(x) is equal to 2, we'll have two general solutions. cosec(x) = 2 when sin(x) = 1/2, so when and sine is also positive in the second quadrant, so also , where n is an integer.

So we have and

If that's a bit confusing, then let n = 0 (just for the purposes of visualising it) and , which is better stated as, since

Hence: which you could state in whatever form you wanted

[deleted]

So for arccos(x)


For arccos(2cosec(x)-3):






cosec(x) is equal to 1 when where n is an integer.
When cosec(x) is equal to 2, we'll have two general solutions. cosec(x) = 2 when sin(x) = 1/2, so when and sine is also positive in the second quadrant, so also , where n is an integer.

So we have and

If that's a bit confusing, then let n = 0 (just for the purposes of visualising it) and , which is better stated as, since

Hence: which you could state in whatever form you wanted

How'd you type all of those cosec and pi values like that?
Is there a tutorial on the forums?

[Conic]

How'd you type all of those cosec and pi values like that?
Is there a tutorial on the forums?

It's called Latex, and there are a few threads on it in the mathematics sub-forum:
List of LaTeX Resources
LaTeX typeset in Maths boards

[Lasercookie]

How'd you type all of those cosec and pi values like that?
Is there a tutorial on the forums?

Yeah, what Conic said. There's a couple of links in my forum signature too, this is kind of a tutorial: How to use LaTeX for typing up maths on ATARNotes

[Phy124]

This can also be a helpful tool for those starting to use LaTeX.

[M-D]

just going back to the math question. what would be the implied range? thanks

[availn]

just going back to the math question. what would be the implied range? thanks

It would be what you said it was, [0,π]. This is because arccos(x) is at its minimum and maximum when x = 1 and -1 respectively. 2cosec(x) - 3 can equate to any number between 1 and -1, so the range of the function is its normal implied domain.

[JMoxey]

This is the exact question that was on the second Calculus 1 assignment at Melbourne Uni.

Breaking Melbourne Uni policy much?